Another full day spent working with Jean-Michel Marin on the new edition of Bayesian Core (soon to be Bayesian Essentials with R!) and the remaining hierarchical Bayes chapter… I have reread and completed the regression and GLM chapters, sent to very friendly colleagues for a last round of comments. Now, I am essentially idle, waiting for Jean-Michel to finish his part on the hierarchical Bayes chapter, so that I can do the final editing.round. Jean-Michel had a very long day on that chapter, leaving Montpellier at 5am to return only at half past midnight, due to massive delays in the train schedule (which is why I always fly to Montpellier…)
Archive for GLMs
This final morning at the ASC 2012 conference in Adelaide, I attended a keynote lecture by Sophia Rabe-Hesketh on GLMs that I particularly appreciated, as I am quite fond of those polymorphous and highly adaptable models (witness the rich variety of applications at the INLA conference in Trondheim last month). I then gave my talk on ABC model choice, trying to cover the three episodes in the series within the allocated 40 minutes (and got from Terry Speed the trivia information that Renfrey Potts, father to the Potts model, spent most of his life in Adelaide, where he died in 2005! Terry added that he used to run along the Torrens river, being a dedicated marathon runner. This makes Adelaide the death place of both R.A. Fisher and R. Potts.)
Later in the morning, Christl Donnelly gave a fascinating talk on her experiences with government bodies during the BSE and foot-and-mouth epidemics in Britain in the past decades. It was followed by a frankly puzzling [keynote Ozcots] talk delivered by Jessica Utts on the issue of parapsychology tests, i.e. the analysis of experiments testing for “psychic powers”. Nothing less. Actually, I first thought this was a pedagogical trick to capture the attention of students and debunk, however Utts’ focus on exhibiting such “powers” was definitely dead serious and she concluded that “psychic functioning appears to be a real effect”. So it came as a shock that she was truly believing in psychic paranormal abilities! I had been under the wrong impression that the 2005 Statistical Science paper of hers was demonstrating the opposite but it clearly belongs to the tradition of controversial Statistical Science that started with the Bible code paper… I also found it flabbergasting to learn that the U.S. Army is/was funding research in this area and is/was actually employing “psychics”, as well that the University of Edinburgh has a parapsychology unit within the department of psychology. (But, after all, UK universities also have long had schools of Divinity, so let the irrational in a while ago!) Read more »
Earlier this month, Daniel Sabanés Bové and Leo Held posted a paper about g-priors on arXiv. While I glanced at it for a few minutes, I did not have the chance to get a proper look at it till last Sunday. The g-prior was first introduced by the late Arnold Zellner for (standard) linear models, but they can be extended to generalised linear models (formalised by the late John Nelder) at little cost. In Bayesian Core, Jean-Michel Marin and I do centre the prior modelling in both linear and generalised linear models around g-priors, using the naïve extension for generalised linear models,
as in the linear case. Indeed, the reasonable alternative would be to include the true information matrix but since it depends on the parameter outside the normal case this is not truly an alternative. Bové and Held propose a slightly different version
where W is a diagonal weight matrix and c is a family dependent scale factor evaluated at the mode 0. As in Liang et al. (2008, JASA) and most of the current literature, they also separate the intercept from the other regression coefficients. They also burn their “improperness joker” by choosing a flat prior on , which means they need to use a proper prior on g, again as Liang et al. (2008, JASA), for the corresponding Bayesian model comparison to be valid. In Bayesian Core, we do not separate from the other regression coefficients and hence are left with one degree of freedom that we spend in choosing an improper prior on g instead. (Hence I do not get the remark of Bové and Held that our choice “prohibits Bayes factor comparisons with the null model“. As argued in Bayesian Core, the factor g being an hyperparameter shared by all models, we can use the same improper prior on g in all models and hence use standard Bayes factors.) In order to achieve closed form expressions, the authors use Cui and George ‘s (2008) prior
which requires the two hyper-hyper-parameters a and b to be specified.
The second part of the paper considers computational issues. It compares the ILA solution of Rue, Martino and Chopin (2009, Series B) with an MCMC solution based on an independent proposal on g resulting from linear interpolations (?). The marginal likelihoods are approximated by Chib and Jeliazkov (2001, JASA) for the MCMC part. Unsurprisingly, ILA does much better, even with a 97% acceptance rate in the MCMC algorithm.
The paper is very well-written and quite informative about the existing literature. It also uses the Pima Indian dataset (The authors even dug out a 1991 paper of mine I had completely forgotten!) I am actually thinking of using the review in our revision of Bayesian Core, even though I think we should stick to our choice of including within the set of parameters…